ORBi Collection: Mathematics
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Hölder Continuity and Wavelets
http://hdl.handle.net/2268/181715
Title: Hölder Continuity and Wavelets
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<br/>Author, co-author: Simons, Laurent
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<br/>Abstract: There exist a lot of continuous nowhere differentiable functions, but these functions do not have the same irregularity. Hölder continuity, and more precisely Hölder exponent, allow to quantify this irregularity. If the Hölder exponent of a function takes several values, the function is said multifractal. In the first part of this thesis, we study in details the regularity and the multifractality of some functions: the Darboux function, the Cantor bijection and a generalization of the Riemann function.
The theory of wavelets notably provides a tool to investigate the Hölder continuity of a function. Wavelets also take part in other contexts. In the second part of this thesis, we consider a nonstationary version of the classical theory of wavelets. More precisely, we study the nonstationary orthonormal bases of wavelets and their construction from a nonstationary multiresolution analysis. We also present the nonstationary continuous wavelet transform.
For some irregular functions, it is difficult to determine its Hölder exponent at each point. In order to get some information about this one, new function spaces based on wavelet leaders have been introduced. In the third and last part of this thesis, we present these new spaces and their first properties. We also define a natural topology on them and we study some properties.Thu, 21 May 2015 08:32:39 GMTSyntactic polygraphs - A formalism extending both constituency and dependency
http://hdl.handle.net/2268/181587
Title: Syntactic polygraphs - A formalism extending both constituency and dependency
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<br/>Author, co-author: Kahane, Sylvain; Mazziotta, Nicolas
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<br/>Abstract: Syntactic analyses describe grouping operations that explain how words are combined to form utterances. The nature of these operations depends on the approach. In a constituency-based approach, grouping operations are ordered, or stratified, part-whole relations. In a dependency-based approach, grouping operations identify a governor (or head), i.e. they are directed hierarchical relations between words. It is possible to convert a constituency tree into a dependency tree by dereifying the nodes, by identifying the governor and by removing the stratification of the part-whole relations. Polygraphs combine the two types of information into a single structure and are therefore a more powerful formalism. By relaxing constraints, polygraphs also allow to underspecify both kinds of information.
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<br/>Commentary: Full paper acceptedMon, 18 May 2015 08:34:18 GMTExtensions du concept de fonction
http://hdl.handle.net/2268/181230
Title: Extensions du concept de fonction
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<br/>Author, co-author: Bair, Jacques; Henry, Valérie
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<br/>Abstract: Extensions modernes du concept de fonction
Comme la plupart des concepts mathématiques, celui de fonction s’est transformé progressivement pour devenir ce qui nous en est enseigné aujourd’hui. Il évolue encore de nos jours : il est toujours plus général, mais également plus abstrait et sophistiqué. Nous donnons ici un petit aperçu intuitif de quelques-unes de ses généralisations modernes.Wed, 06 May 2015 12:12:34 GMTPetit voyage à travers les âges: de l'expression à la fonction
http://hdl.handle.net/2268/181228
Title: Petit voyage à travers les âges: de l'expression à la fonction
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<br/>Author, co-author: Bair, Jacques; Henry, Valérie
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<br/>Abstract: Le concept de fonction est assurément fondamental en mathématiques. Il a été construit lentement, par de multiples améliorations successives. Dans cet article, nous souhaitons évoquer succinctement quelques étapes marquantes de son élaboration.Wed, 06 May 2015 12:01:05 GMTDes statistiques pour détecter les équipements de laboratoire peu fiables
http://hdl.handle.net/2268/181141
Title: Des statistiques pour détecter les équipements de laboratoire peu fiables
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<br/>Author, co-author: Aerts, StéphanieMon, 04 May 2015 10:01:55 GMTPar A plus B
http://hdl.handle.net/2268/180796
Title: Par A plus B
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<br/>Author, co-author: Deliège, Adrien; Nicolay, Samuel
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<br/>Abstract: Exposé de vulgarisation sur l'état de l'art concernant les ondelettes et ses applications, en particulier l'étude du phénomène El Niño.Wed, 22 Apr 2015 19:25:05 GMTEGU2015 - ENSO forecast using a wavelet-based mode decomposition
http://hdl.handle.net/2268/180789
Title: EGU2015 - ENSO forecast using a wavelet-based mode decomposition
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<br/>Author, co-author: Deliège, Adrien; Nicolay, Samuel; Fettweis, Xavier
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<br/>Abstract: The aim of this work is to introduce a new method for forecasting major El Niño/ La Niña events with the use of a wavelet-based mode decomposition. These major events are related to sea surface temperature anomalies in the tropical Pacific Ocean: anomalous warmings are known as El Niño events, while excessive coolings are referred as La Niña episodes. These climatological
phenomena are of primary importance since they are involved in many teleconnections ; predicting them long before they occur is therefore a crucial concern.
First, we perform a wavelet transform (WT) of the monthly sampled El Niño Southern Oscillation 3.4 index (from 1950 to present) and compute the associated scale spectrum, which can be seen as the energy carried in the WT as a function of the scale. It can be observed that the spectrum reaches five peaks, corresponding to time scales of about 7, 20, 31, 43 and 61 months
respectively. Therefore, the Niño 3.4 signal can be decomposed into five dominant oscillating components with time-varying amplitudes, these latter being given by the modulus of the WT at the associated pseudo-periods. The reconstruction of the index based on these five components is accurate since more than 93% of the El Niño/ La Niña events of the last 60 years are recovered and no major event is erroneously predicted. Then, the components are smoothly extrapolated using polynomials and added together, giving so several years forecasts of the Niño 3.4 index. In order to increase the reliability of the forecasts, we perform several months
hindcasts (i.e. retroactive probing forecasts) which can be validated with the existing data. It turns out that most of the major events can be accurately predicted up to three years in advance, which makes our methodology competitive for such forecasts.
Finally, we discuss the El Niño conditions currently undergone and give indications about the next La Niña event.Wed, 22 Apr 2015 15:11:26 GMTTesting the proportional odds assumption in multiply imputed ordinal longitudinal data
http://hdl.handle.net/2268/179868
Title: Testing the proportional odds assumption in multiply imputed ordinal longitudinal data
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<br/>Author, co-author: Donneau, Anne-Françoise; Mauer, M; Lambert, Philippe; Lesaffre, E.; Albert, AdelinWed, 01 Apr 2015 07:37:30 GMTLaTeX, un peu, beaucoup (7. Tableaux (encore))
http://hdl.handle.net/2268/179732
Title: LaTeX, un peu, beaucoup (7. Tableaux (encore))
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<br/>Author, co-author: Dupont, PascalFri, 27 Mar 2015 21:54:14 GMTLaTeX, un peu, beaucoup (6. Tableaux)
http://hdl.handle.net/2268/179731
Title: LaTeX, un peu, beaucoup (6. Tableaux)
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<br/>Author, co-author: Dupont, PascalFri, 27 Mar 2015 21:42:08 GMTLaTeX, un peu, beaucoup (5. Les macros)
http://hdl.handle.net/2268/179730
Title: LaTeX, un peu, beaucoup (5. Les macros)
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<br/>Author, co-author: Dupont, PascalFri, 27 Mar 2015 21:29:11 GMTÉvolutions et initiatives contribuant à faire vivre les maths comme une discipline vivante accessible à tous : le cas de la Belgique
http://hdl.handle.net/2268/179627
Title: Évolutions et initiatives contribuant à faire vivre les maths comme une discipline vivante accessible à tous : le cas de la Belgique
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<br/>Author, co-author: Henry, ValérieThu, 26 Mar 2015 07:28:50 GMTAngles corniculaires et de demi-cercle chez Euclide
http://hdl.handle.net/2268/179515
Title: Angles corniculaires et de demi-cercle chez Euclide
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<br/>Author, co-author: Bair, Jacques; Henry, Valérie
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<br/>Abstract: Dans cet article, on examine comment Euclide présentait, dans ses Eléments, les notions liées au concept d'angle dans le plan. Il considérait des angles mixtilignes, en particulier corniculaires et de demi-cercle, qui peuvent être de nos jours exploités pour introduire les nombres hyperréels intervenant en analyse non standard.Mon, 23 Mar 2015 09:44:19 GMTGraded-commutative nonassociative algebras: higher octonions and Krichever-Novikov superalgebras; their structures, combinatorics and non-trivial cocycles.
http://hdl.handle.net/2268/179471
Title: Graded-commutative nonassociative algebras: higher octonions and Krichever-Novikov superalgebras; their structures, combinatorics and non-trivial cocycles.
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<br/>Author, co-author: Kreusch, Marie
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<br/>Abstract: This dissertation consists of two parts.
The first one is the study of a series of real (resp. complex) noncommutative and nonassociative algebras $\bbO_{p,q}$ (resp. $\bbO_{n}$) generalizing the algebra of octonion numbers $\bbO$. This generalization is similar to the one of the algebra of quaternion numbers in Clifford algebras.
Introduced by Morier-Genoud and Ovsienko, these algebras have a natural $\bbZ_2^n$-grading ($p+q =n$), and they are characterized by a cubic form over the field $\bbZ_2.$
We establish all the possible isomorphisms between the algebras $\bbO_{p,q}$
preserving the structure of $\bbZ_2^n$-graded algebra.
The classification table of $\bbO_{p,q}$ is quite similar to that of
the real Clifford algebras $\cC l_{p,q}$,
the main difference is that the algebras $\bbO_{n,0}$ and $\bbO_{0,n}$ are exceptional.
We also provide a periodicity for the algebras $\bbO_n$ and $\bbO_{p,q}$ analogous to the periodicity for the Clifford algebras $\cC l_{n}$ and $\cC l_{p,q}$. In the second part we consider superalgebras of Krichever-Novikov (K-N) type.
Krichever and Novikov introduced a family of Lie algebras with two marked points generalizing the Witt algebra and its central extension called the Virasoro algebra. The K-N Lie (super)algebras for more than two marked points were studied by Schlichenmaier.
In particular, he extended the explicit formula of $2$-cocycles due to Krichever and Novikov to multiple-point situation.
We give an explicit construction of central extensions of Lie superalgebras of K-N type and we establish a $1$-cocycle with values in its dual space.
In the case of Jordan superalgebras related to superalgebras of K-N type, we calculate a 1-cocycle with coefficients in the dual space.Thu, 19 Mar 2015 15:25:06 GMTA comparison of within-season yield prediction algorithms based on crop model behaviour analysis
http://hdl.handle.net/2268/178919
Title: A comparison of within-season yield prediction algorithms based on crop model behaviour analysis
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<br/>Author, co-author: Dumont, Benjamin; Basso, Bruno; Leemans, Vincent; Bodson, Bernard; Destain, Jean-Pierre; Destain, Marie-France
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<br/>Abstract: The development of methodologies for predicting crop yield, in real-time and in response to different agro-climatic conditions, could help to improve the farm management decision process by providing an analysis of expected yields in relation to the costs of investment in particular practices. Based on the use of crop models, this paper compares the ability of two methodologies to predict wheat yield (Triticum aestivum L.), one based on stochastically generated climatic data and the other on mean climate data. It was shown that the numerical experimental yield distribution could be considered as a log-normal distribution. This function is representative of the overall model behaviour. The lack of statistical differences between the numerical realisations and the logistic curve showed in turn that the Generalised Central Limit Theorem (GCLT) was applicable to our case study. In addition, the predictions obtained using both climatic inputs were found to be similar at the inter and intra-annual time-steps, with the root mean square and normalised deviation values below an acceptable level of 10% in 90% of the climatic situations. The predictive observed lead-times were also similar for both approaches. Given (i) the mathematical formulation of crop models, (ii) the applicability of the CLT and GLTC to the climatic inputs and model outputs, respectively, and (iii) the equivalence of the predictive abilities, it could be concluded that the two methodologies were equally valid in terms of yield prediction. These observations indicated that the Convergence in Law Theorem was applicable in this case study. For purely predictive purposes, the findings favoured an algorithm based on a mean climate approach, which needed far less time (by 300-fold) to run and converge on same predictive lead time than the stochastic approach.Thu, 05 Mar 2015 05:31:41 GMTSpecial issue dedicated to the 14th "Journées montoises d'informatique théorique"
http://hdl.handle.net/2268/178709
Title: Special issue dedicated to the 14th "Journées montoises d'informatique théorique"
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<br/>Editor: Bruyère, Véronique; Jungers, Raphaël; Hollanders; Rigo, Michel
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<br/>Commentary: The conference was held in Louvain-La-Neuve, September 11th - 14th, 2012Thu, 26 Feb 2015 09:52:32 GMTSpecial issue dedicated to the second "AutoMathA conference"
http://hdl.handle.net/2268/178707
Title: Special issue dedicated to the second "AutoMathA conference"
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<br/>Editor: Bruyère, Véronique; Pin, Jean-Eric; Restivo, Antonio; Rigo, Michel
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<br/>Commentary: The conference was held in Liège June 8-12, 2009.Thu, 26 Feb 2015 09:48:19 GMTDefining multiplication in some additive expansions of polynomial rings
http://hdl.handle.net/2268/178705
Title: Defining multiplication in some additive expansions of polynomial rings
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<br/>Author, co-author: Point, Françoise; Rigo, Michel; Waxweiler, Laurent
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<br/>Abstract: Adapting a result of R. Villemaire on expansions of Presburger arithmetic, we show how to define multiplication in some expansions of the additive reduct of certain Euclidean rings. In particular, this applies to polynomial rings over a finite field.Thu, 26 Feb 2015 09:27:58 GMTAnother Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words (long version)
http://hdl.handle.net/2268/178703
Title: Another Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words (long version)
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<br/>Author, co-author: Rigo, Michel; Salimov, Pavel
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<br/>Abstract: The binomial coefficient of two words $u$ and $v$ is the number of times $v$ occurs as a subsequence of $u$. Based on this classical notion, we introduce the $m$-binomial equivalence of two words refining the abelian equivalence. Two words $x$ and $y$ are $m$-binomially equivalent, if, for all words $v$ of length at most $m$, the binomial coefficients of $x$ and $v$ and respectively, $y$ and $v$ are equal. The $m$-binomial complexity of an infinite word $x$ maps an integer $n$ to the number of $m$-binomial equivalence classes of factors of length $n$
occurring in $x$. We study the first properties of $m$-binomial equivalence. We compute the $m$-binomial complexity of two classes of words: Sturmian words and (pure) morphic words that are fixed points of Parikh-constant morphisms like the Thue--Morse word, i.e., images by the morphism of all the letters have the same Parikh vector. We prove that the frequency of each symbol of an infinite recurrent word with bounded $2$-binomial complexity is rational.
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<br/>Commentary: This is an extended version of the conference version. In particular, it contains a new discussion about frequencies of symbols when the $2$-binomial complexity is bounded.Thu, 26 Feb 2015 09:23:51 GMTAvoiding 2-binomial squares and cubes
http://hdl.handle.net/2268/178702
Title: Avoiding 2-binomial squares and cubes
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<br/>Author, co-author: Rao, Michaël; Rigo, Michel; Salimov, Pavel
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<br/>Abstract: Two finite words $u,v$ are $2$-binomially equivalent if, for all words $x$ of length at most $2$, the number of occurrences of $x$ as a (scattered) subword of $u$ is equal to the number of occurrences of $x$ in $v$. This notion is a refinement of the usual abelian equivalence. A $2$-binomial square is a word $uv$ where $u$ and $v$ are $2$-binomially equivalent.
In this paper, considering pure morphic words, we prove that $2$-binomial squares (resp. cubes) are avoidable over a $3$-letter (resp. $2$-letter) alphabet. The sizes of the alphabets are optimal.Thu, 26 Feb 2015 09:18:25 GMT